A349642 Smallest prime such that the next n prime gaps are in arithmetic progression.

2, 2, 2, 17, 347, 2903, 15373, 128981, 19641263, 245333213, 245333213, 27797667517, 68439250465123, 68439250465123

Offset

0,1

Comments

Equivalently, a(n) is the smallest prime p = prime(k) such that there is a polynomial f of degree at most 2 such that f(j) = prime(j) for k <= j <= k + n.

Any sequence of at most 2 terms is considered to be a degenerate arithmetic progression, so a(n) = 2 (the smallest prime) for n <= 2.

a(n) is the smallest prime p = prime(k) such that A036263(k) = A036263(k+1) = ... = A036263(k+n-2).

Links

Table of n, a(n) for n=0..13.

Example

The three prime gaps following the prime 17 are 2, 4, and 6, which are in arithmetic progression. This is not true for any smaller prime, so a(3) = 17.
The eight prime gaps following the prime 19641263 are 20, 18, 16, 14, 12, 10, 8, and 6, which are in arithmetic progression. This is not true for any smaller prime, so a(8) = 19641263.

Crossrefs

From n = 3, second row of A349644.

Cf. A001223, A006560, A036263, A348927.

Sequence in context: A195871 A214756 A079007 * A064215 A358633 A087238

Adjacent sequences: A349639 A349640 A349641 * A349643 A349644 A349645

Keyword

nonn,more

Author

Pontus von Brömssen, Nov 23 2021

Extensions

a(12)-a(13) from Martin Ehrenstein, Dec 05 2021

Status

approved